This thesis details investigations in the use of stochastic phase space methods to study driven dissipative quantum systems. While these methods are useful in a wide array of physical contexts, the work I present here is primarily concerned with exciton-polaritons in semiconductor microcavities, quasiparticles that result from the strong coupling between photons confined to the cavity and excitons in the quantum well layer. Exciton-polaritons have all of the archetypal properties of open many-body quantum systems: driving by an external laser, dissipation from photons escaping the cavity, and nonlinearity from the interactions between excitons. Two different stochastic phase space methods are explored in this thesis. The truncated Wigner method is a semiclassical method, in the sense that it neglects some quantum correlations, which is already widely used to simulate polariton systems. Here, I use it to study the optical parametric oscillator (OPO) regime, where polaritons from the driven mode scatter to coherently occupy additional modes. I first explore the variations in momentum structures in the OPO regime with the drive strength, before then studying the spatial correlations, finding the first numerical evidence of the 2D Kardar-Parisi-Zhang universality, a universality class unique to non-equilibrium systems, in polariton OPO. I next employ the positive-P method, which provides fully quantum and scalable numerical simulations of open quantum systems. I investigate stronger quantum correlations that can arise from interference effects in driven-dissipative Bose-Hubbard Lieb lattices, using physical parameters accessible to current polariton micropillar experiments. Finally, I outline preliminary investigations into adapting the positive-P method to models with coupled bosons and qubits, relevant to experiments in superconducting circuit QED.